Problem: Rewrite as a simplified fraction. ${3.\overline{5} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 35.5555...\\ 1x &= 3.5555...\end{align*}}$ Subtracting the two equations, we have: ${9x = 32}$ ${x = \dfrac{32}{9}} \text{or} {3 \dfrac{5}{9}}$